Because flaps need a large angle of displacement and only go down the proper way is to incline the angle of the control horn forward for top drive flaps. That way your horn reaches the vertical line at half deployment and you are still working with the "stronger" angle for controlling the flap. For example assuming an 80 degree max down deflection your control horn hole should be swept forward by 40 degrees. Then at full deflection it is swept back by 40 degrees. In this manner you're working with the stronger angles of deflection and will have lots of resistance to the airflow. It will also give you the most linear response to the stick angles. And because you're also minimizing the angle between the pushrod and the control horn so that it stays as close to 90 as practical you are reducing the effect of any slop.

With a regular style horn which sits at 90 degrees to the control surface by the time you get 80 degrees of deflection the pushrod is just about along the same line as the horn's axis. At this point any amount of flex or slop at all will be strongly magnified. In addition there is very little holding power to control the surface.

There is no optimum angle. For minimum slop the rule is the same as for any other surface: horn perpendicular to pushrod/hinge. The difference with flaps is that the clevis will hit the bottom skin of the wing if setup this way so you need the horn forward of the hinge by however much is required for the maximum deflection you want.

But in total there are four things to optimize:
- Flap horn as tall as practical
- Horn as close to perpendicular as your max deflection will allow
- Stiffness of servo/mounting/wingskin/pushrod
- Servo horn the right length

Vespa, for any normal surface that normally sits at the middle of its travel angle I would agree. But a flap is different. A flap sits at one extreme of its throw for normal flight and at the other extreme for when fully deployed. So the rules change for flaps. Instead you want the angle to be swept as I explained so that when the flap is at the middle of it's range of travel THEN it is at 90 degrees to the chord line.

No rules change. Minimum slop and maximum holding power occur at the point where the horn is perpendicular to the pushrod/hinge and you want this to occur near the nominal position. What you describe is a way to reduce servo loads with very large flap deflections. But since flaps are not typically deployed at high speeds it's more important to improve performance around the neutral position rather than at full deflection.

The question I have for the OP is less slop and more holding power at what condition, flaps retracted (zero deflection) or flaps extended?

I set mine up much as Bruce describes, with one addition. I set my servo arm just forward of 90 deg with flaps zero and pointed well back with flaps extended for greater mechanical advantage when the flaps are highly loaded. I am less concerned with linearity and more so with servo torque load.

Vespa, I've seen flaps done as you suggest. The issue is that the deflection is so affected by small differences when the horn axis is almost in line with the pushrod that it's nearly impossible to achieve the same deflection angle from side to side. Also with so little displacement distance between the pushrod and the hinge line the flap is easily "flexed" through quite an angle.

Indeed, it's all a balance of compromises. You can sacrifice some precision around neutral to gain some precision at full deflection, and to some extent this needs to be done depending on the strength of the wing and your intended use. You usually don't want to take it right to the limit where the clevis hits the bottom wing skin at full flap deflection because the flex and hinge/pushrod loads will be substantial. But you really don't need much precision beyond 70-80 degrees of deflection so I advocate biasing the linkage to work best where you need it most -- camber, flaperon, and high-speed flutter resistance. The symmetry issue is annoying, but it's really not noticeable in flight and most radios can curve it out anyway.

You make a wise and good point about the importance of rigidity and precision around neutral. A perfect example is on high performance pure and electric sailplanes that use full span camber changing to make the wing more efficient. A high degree of rigidity and precision is essential.

The problem is that as the flap extends to near 80 or so degrees down it is not only the precision that suffers. The system loses its mechanical advantage as the angle between control horn axis and pushrod becomes close to the same. This means the servo has to work harder to hold it there against whatever air speed loads are created. On some models that use flaps and that are flown aggresively concern for this cannot be minimized. Competition sailplanes and glider tugs are just two examples of models that use flaps for serious speed control and dive down at very steep angles and higher airspeeds with flaps fully extended.

Perhaps a compromise? Something like 20 degrees swept forward would still provide a good degree of power and precision for angles close to zero. For example competition gliders and serious electrics where they want to run from around +5 to -10 to -15 for various tasks. This would result in a 60 degree swept back angle for the horn when the flaps are fully deflected to 80 degrees. Such an angle is still not ideal. But it's far better than the sort of leverage loss that comes from angling down to a mere 10 degrees.